Future Value

Future Value Of A Single Amount

Future Value is the amount of money that an investment made today (the
present value) will grow to by some future date. Since money has time value, we naturally
expect the future value to be greater than the present value.
The difference between the two depends on the number of compounding
periods involved and the going interest rate.

The relationship between the future value and present value can
be expressed as:

FV = PV (1 + i)n

Where:

FV = Future Value

PV = Present Value

i = Interest Rate Per Period

n = Number of Compounding Periods

Example: You can afford to put $10,000 in a savings account
today that pays 6% interest compounded annually. How much will you have 5
years from now if you make no withdrawals?

PV = 10,000
i = .06
n = 5

FV = 10,000 (1 + .06)5 = 10,000
(1.3382255776) = 13,382.26

End of Year

1

2

3

4

5

Principal

10,000.00

10,600.00

11,236.00

11,910.16

12,624.77

Interest

600.00

636.00

674.16

714.61

757.49

Total

10,600.00

11,236.00

11,910.16

12,624.77

13,382.26

Example 2: Another financial institution offers to pay 6%
compounded semiannually. How much will your $10,000 grow to in five
years at this rate?

Interest is compounded twice per year so you must divide the annual interest
rate by two to obtain a rate per period of 3%. Since there are two
compounding periods per year, you must multiply the number of years by two
to obtain the total number of periods.